Stabilizer states are extensively studied in quantum information theory fortheir structures based on the Pauli group. Calderbank-Shor-Steane (CSS)stabilizer states are of particular importance in their application tofault-tolerant quantum computation (FTQC). However, how to fault-tolerantlyprepare arbitrary CSS stabilizer states for general CSS stabilizer codes isstill unknown, and their preparation can be highly costly in computationalresources. In this paper, we show how to prepare a large class of CSSstabilizer states useful for FTQC. We propose distillation protocols usingsyndrome encoding by classical codes or quantum CSS codes. Along the samelines, we show that classical coding techniques can reduce the ancillaconsumption in Steane syndrome extraction by using additional transversalcontrolled-NOT gates and classical computing power. In the scenario of a fixedancilla consumption rate, we can increase the frequency of quantum errorcorrection and effectively lower the error rate.
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